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\(D\delta\)-supercontinuous functions. (English) Zbl 1036.54003
Since 1960, when N. Levin [Am. Math. Mon. 67, 269 (1960; Zbl 0156.43305)] introduced the class of strongly continuous mappings (the image of the closure of any subset \(A\) of the domain is contained in the image of \(A\)), a number of strong forms of continuity (but weaker than strong continuity) have been introduced and investigated. In this paper the authors introduce one more strong form of continuity, weaker than strong continuity and called \(D_\delta\)-supercontinuity. Basic properties of these mappings are investigated, in particular their relationships with other strong variants of continuity and with \(\delta\)-completely regular spaces (a class of spaces wider than the class of completely regular spaces) introduced by the same authors in a recent paper.

54C05 Continuous maps
54D15 Higher separation axioms (completely regular, normal, perfectly or collectionwise normal, etc.)